The Linearized Fixed Gravimetric Boundary Value Problem and Its Solution in Spheroidal Approximation

Abstract

In this work, the linearized fixed gravimetric boundary value problem and its solution in spheroidal approximation is discussed. Input to the problem are gravity disturbances, using the known Earth’s topography as a boundary, so this corresponds to an oblique derivative problem. From the physical viewpoint, it has many advantages and can serve as the basis in establishing a world height system that supports geometrical and physical heights world-wide with high precision. Adopting the spheroidal approximation, an integral equation results which can be solved using successive approximations. The mathematical model becomes simpler and can be solved more easily by neglecting the Earth’s topography. On the other hand, adopting the spherical approximation, the solution corresponds to a normal derivative problem plus suitable corrections which include the topography. We conclude that the spheroidal approximation should be taken into account in order to achieve higher accuracy.